vergangen
past
Refers to something that lies in the past, has happened, or no longer exists; previous.
In den vergangenen Wochen hat es kaum geregnet.
In the past few weeks, it has hardly rained.

past
Loading your saved state.
past
Refers to something that lies in the past, has happened, or no longer exists; previous.
In den vergangenen Wochen hat es kaum geregnet.
In the past few weeks, it has hardly rained.

'Vergangen' (past) is the past participle of the verb 'vergehen', which means 'to pass' (for time). It is used like an adjective to express that something belongs to the past.
Die Zeit vergeht so schnell, schon wieder ist ein Jahr vergangen.
Time passes so quickly; another year has already passed.
The adjective 'vergangen' (past) is almost always combined with nouns that describe a period of time. Typical combinations are 'vergangene Woche' (last week), 'vergangener Monat' (last month), or 'vergangenes Jahr' (last year).
Am vergangenen Wochenende war ich im Museum.
Last weekend I was at the museum.
'Vergangen' (past) is mainly used attributively, meaning it stands before a noun and is declined like a normal adjective. Predicative use ('Die Zeit ist vergangen' — time has passed) is usually part of the perfect tense of the verb 'vergehen' (to pass).
Die Ereignisse der vergangenen Tage haben alle überrascht.
The events of the past few days surprised everyone.
last
'letzt' and 'vergangen' can both talk about something that lies before the present point in time. 'letzt' usually means the directly preceding time, for example 'letzte Woche' (last week) or 'letztes Jahr' (last year). 'vergangen' is more general and only emphasizes that something is over or lies in the past. Learners may confuse the words because both look back in time. A practical tip: 'letzt' fits when you mean the previous period; 'vergangen' fits when you want to emphasize more strongly that something is no longer current.

In den vergangenen Monaten hatte Laura oft Kopfschmerzen.
In the past few months, Laura often had headaches.
Letzte Woche hat Frau Neumann mit der Klasse ein neues Thema begonnen.
Last week, Ms. Neumann started a new topic with the class.